What I really would need now is a set of step-by-step instructions to upgrade Lazarus to 1.8.4 on the Raspberry Pi 3B with Raspbian Stretch...

I develop and debug on the Kubuntu Linux on the PC, then I transfer all the source to the Raspberry for a final compilation and testing. For this, I need that the two Lazarus versions (PC and Raspberry) are kept in sync....

I have tried the default deb package and also picked the three separate programs from sourceforge.

The fpc installation was pretty fast and I got the compiler running.But when I click on the lazarus deb package (lazarus-project_1.8.4-0_amd64.deb), it just vanishes without proper response. It doesn't give any errors.

Installing Lazarus on Linux, especially Ubuntu can be tricky sometimes. If you have followed the tutorial but still can't install it, please provide more information so I may be able to do some tests to understand the problem. But as you said it just vanished without any response, it seems you have use the version provided by your Ubuntu repository.

Ubuntu has a version of FPC in the repository. if you update it, the new version installed becomes "fpc 3.0.4+dfsg-18ubuntu1".the current deb requires fpc = 3.0.4 as dependency.Change the control file of the DEBIAN folder to ">=" :

The fpc installation was pretty fast and I got the compiler running.But when I click on the lazarus deb package (lazarus-project_1.8.4-0_amd64.deb), it just vanishes without proper response. It doesn't give any errors.

Usually SourceForge has the latest stable release of Lazarus. But after a while Ubuntu repository will catch up too.

The packages on SourceForge and Ubuntu repository are not exactly identical, combining them usually will cause problem. And that is one of the reasons to fail if you try to install Lazarus when using latest version downloaded from SourceForge. It (the Ubuntu) may 'force' you use the FPC in the Ubuntu repository. Not always but some in my tests, I had to disconnect my internet connection or it won't able to install successfully.

And of course, if the version of Lazarus you wish to install is already in the Ubuntu repository, using it is the easiest way to install Lazarus.